Question: Multiply.
Answer: $71 \times 8{,}124$ and $7.1\times 81.24$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $71 \times 8{,}124$. Then we can estimate to place the decimal point in the product of $7.1\times 81.24$. $\begin{aligned} 8{,}124&\\ \underline{ \times 71}&\\ 4}& {1} \times {4\text{ ones}}\\ 20}& {1} \times {2\text{ tens}}\\ 100}& {1} \times {1 \text{ hundred}}\\ 8{,}000}& {1} \times {8 \text{ thousands}}\\ 280}& {70} \times {4 \text{ ones}}\\ 1{,}400}& {70} \times{2\text{ tens}}\\ 7{,}000}& {70} \times {1\text{ hundred}}\\ \underline{+560{,}000}}& {70} \times {8\text{ thousands}}\\ 576{,}804 \end{aligned}$ $71 \times 8{,}124 = 576{,}804$ Let's estimate to place the decimal in $7.1 \times 81.24$. $\begin{aligned} 7.1 \times 81.24 &\approx 7 \times 80\\\\ &\approx 560 \end{aligned}$ Where can we place the decimal in $576{,}804$ to get a product close to $560$ ? $576.804 = 7.1 \times 81.24$